CEE 370 Environmental Engineering Principles Lecture #32 - - PDF document

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CEE 370 Environmental Engineering Principles Lecture #32 - - PDF document

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CEE 370 Lecture #32 11/26/2019 Print version Updated: 26 November 2019 CEE 370 Environmental Engineering Principles Lecture #32 Wastewater Treatment III: Process Modeling & Residuals Reading M&Z: Chapter 9 Reading: Davis &

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 1

David Reckhow CEE 370 L#32 1

CEE 370 Environmental Engineering Principles

Lecture #32 Wastewater Treatment III: Process Modeling & Residuals

Reading M&Z: Chapter 9

Reading: Davis & Cornwall, Chapt 6-1 to 6-8

Reading: Davis & Masten, Chapter 11-11 to 11-12 Updated: 26 November 2019

Print version

David Reckhow

CEE 370 L#32

2

Microbial Biomass in a CMFR

dm dt = (C Q ) (C Q ) r V

A i=1 n Ai i in j=1 n Aj j

  • ut

A

 

 

CA V

CA0 Q0 CA Q0

General Reactor mass balance

But with CMFRs we have a single outlet concentration (CA) and usually a single inlet flow as well

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 2

David Reckhow

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Batch Microbial Growth

CA V

1 V dM dt = - r

A A

A i=1 n Ai i in j=1 n Aj j

  • ut

A

dM dt = (C Q ) (C Q )

  • r V

 

 Because there isn’t any flow in a batch reactor:

A A

dC dt = - r

And: Batch reactors are usually filled, allowed to react, then emptied for the next batch

General Reactor mass balance

X kX

For 1st order biomass growth

David Reckhow

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Batch Microbial Growth

 Observed behavior

Time Lag Stationary Death Exponential Growth Covered in lecture #17

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David Reckhow

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Exponential Growth model

where, X = concentration of microorganisms at time t t = time  = proportionality constant or specific growth rate, [time─1] dX/dt = microbial growth rate, [mass per volume-time] N r t dN/dt

D&M Text

X dt dX

gr

       

Covered in lecture #17

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  • Exp. Growth (cont.)

ln X X = t

     

X = X e

  • t

  • r

X dt dX

gr

        dt X dX

gr

       

Covered in lecture #17

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 4

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Substrate-limited Growth

 Also known as resource-limited growth

 THE MONOD MODEL

where, max = maximum specific growth rate, [day-1] S = concentration of limiting substrate, [mg/L] Ks = Monod or half-velocity constant, or half saturation coefficient, [mg/L]

S K SX X dt dX

S gr

        

max

 

S K S

S 

max

 

and

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Monod Kinetics

0.5*µm KS

Covered in lecture #17

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 5

Substrate Utilization & Yield

David Reckhow

CEE 370 L#32

9 H&H, Fig 11-38, pp.406

 Related to growth by Y, the yield coefficient

 Mass of cells produced

per mass of substrate utilized

 Just pertains to cell growth

dt dS dt dX S X Y    

dt dS Y dt dX

gr

      

Microbial Growth

 Monod kinetics in a chemostat (batch reactor)

 Where

 dS/dt = rsu = actual substrate utilization rate  k = maximum substrate utilization rate = μmax/Y  S = concentration of substrate (Se in H&H)  KS = half-saturation constant  Y = cell yield = dX/dS

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e S e su

S K XS k r   S K SX X dt dX

S gr

        

max

  S K XS Y dt dS

S 

max

& Divide by Y Substitute for dS

dt dS Y dt dX

gr

      

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 6

Death

 Bacterial cells also die at a characteristic

first order rate with a rate constant, k

 This occurs at all times, and is

independent of the substrate concentration

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X k dt dX

d d

       

Overall model: chemostat

 Combining growth and death, we have:  And in terms of substrate utilization

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X k S K SX dt dX dt dX dt dX

d S d gr net

                      

max

 X k dt dS Y dt dX

d net

              dt dS dt dX Y

gr

       

See: M&Z equ 9.3

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Activated Sludge Flow Schematic

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Aeration

Basin

V,X Settling

Tank Xo So X S Xe S Qr Xr Q Qw Xr S

 Conventional

Return activated sludge Waste activated sludge

Influent Effluent

Q+ Qr

Efficiency & HRT

 Efficiency of BOD removal  Hydraulic Retention Time, HRT (Aeration Time)

 Same as retention time in DWT (tR)  Actual HRT is a bit different

 Isn’t used as much in design David Reckhow CEE 370 L#32

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 

  • S

S S E % 100  

Q V  

R act

Q Q V   

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 8

SRT – solids retention time & R

 SRT: Primary operation and design parameter

 How long does biomass stay in system  Typically equals 5-15 days

 Recycle Ratio

 Values of 0.25-1.0 are typical

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 

r w r w e w c

X Q XV X Q X Q Q XV     

Q Q R

r

See: M&Z equ 9.10

F:M Ratio and volumetric loading

 Food-to-Microorganism Ratio (F/M)

 Typical values are 0.2-0.6 in complete mixed AS

 BOD volumetric Loading

 Typically 50-120 lb BOD/day/1000ft3 tank volume

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X V BOD Q M F   

XV QS M F

V QS Loading

M&Z equ 9.16

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 9

  • Act. Sludge: Biomass Model

 Steady State mass balance on biomass

 Incorporating the chemostat model gets:  And simplifying

 Finally, we recognize that the amount of solids entering with the WW (i.e.,

Xo) and leaving in the treated effluent (i.e., Xe) is quite small and can be neglected

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batch r w e e

  • dt

dX V X Q X Q QX dt dX V            0

X k S K SX dt dX dt dX dt dX

d S d gr net

                      

max

From chemostat model

               X k S K SX V X Q X Q QX dt dX V

d S r w e e

  • max

               X k S K SX V X Q X Q QX

d S r w e e

  • max

Biomass Model II

 So it becomes  And rearranging

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           X k S K SX V X Q

d S r w max

d S r w

k S K S VX X Q   

max

 

r w r w e w c

X Q XV X Q X Q Q XV     

c

 1

Earlier equation for SRT

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 10

  • Act. Sludge: Substrate Model

 Steady state mass balance on substrate

 Substituting and noting that Qe=Q-Qw  And further simplifying

David Reckhow

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batch w e

  • dt

dS V S Q S Q QS dt dS V            0

From chemostat model

S K XS Y dt dS

S 

max

              S K XS Y V S Q S Q QS QS

S w w

  • max

 

           S K XS Y V S S Q

S

  • max

Merging the biomass & substrate models

If we divide the previous equation by V and X

Multiply both sides by Y

Now insert the LH term into the earlier equation based on biomass

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 

           S K XS Y V S S Q

S

  • max

 

S K S Y VX S S Q

S

 

max

d S r w c

k S K S VX X Q    

max

1  

 

S K S VX S S YQ

S

 

max

 

d

  • r

w c

k VX S S YQ VX X Q      1

M&Z equ 9.8 M&Z equ 9.9

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CEE 370 Lecture #32 11/26/2019 Lecture #32 Dave Reckhow 11

Combined model II

 Now recognize that Q/V is the reciprocal of

the HRT

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 

d

  • c

k X S S Y      1 1

Question

 All else being equal, as SRT goes up:

1.

Settleability goes down

2.

F/M goes down

3.

Waste sludge return ratio must go down

4.

Endogenous respiration becomes less important

5.

Sludge yield increases

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Aeration: Loadings

 Food-to-Microorganism

Ratio (F/M)

 Sludge Age or mean cell

residence time (ɵc)

Where

Q=WW flow

V=volume of aeration tank

X=MLVSS=mixed liquor volatile suspended solids (biomass concentration)

Xe=VSSe = suspended solids in wastewater effluent

XW=VSSw = suspended solids in waste sludge

Qw = flow of waste sludge

SS is sometimes used instead

  • f VSS

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X V BOD Q M F   

   

W W W W e e c

Q X VX Q X Q X VX    

Operating Criteria

 Loading, biomass, retention time, etc

David Reckhow

CEE 370 L#32

24 H&H, Table11-4, pp.395

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Activated Sludge

 Mixed liquor  Return Activated sludge

  • 1. Surface aerators
  • 2. Bubble diffusers

David Reckhow CEE 370 L#32 26

CEE 370 Environmental Engineering Principles

Lecture #32b Wastewater Treatment IIIb: Process Modeling & Residuals

Reading: M&Z Chapter 9.11

Other Reading: Davis & Cornwall, Chapt 6-1 to 6-8 and Davis & Masten, Chapter 11-11 to 11-12 Updated: 26 November 2019

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Anaerobic Digester Problem

Anaerobic digesters are commonly used in wastewater

  • treatment. The biological process produces both

carbon dioxide and methane gases. A laboratory worker plans to make a "synthetic" digester gas. There is currently 2 L of methane gas at 1.5 atm and 1 L of carbon dioxide gas at 1 atm in the lab. If these two samples are mixed in a 4 L tank, what will be the partial pressures of the individual gases? The total pressure?

Example 4.4 from Ray

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28 t CH CO

P = P + P = 1 atm

4 2

2

P = 1 atm 1 L 4 L = 0.25 atm      

2

P = 1.5 atm 2 L 4 L = 0.75 atm      

Solution to Anaerobic Digester Problem

First, we must find the partial pressures of the individual gases using the ideal gas law:

1 1 2 2

P V = nRT = P V

2 1 1 2

P = P V V      

For methane gas For carbon dioxide gas: And the total is:

  • r
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Solids Balance

SRT XV Q X

w u

  mass of organisms in tank mass of organisms removed per day

HRT V Q 

Sludge Secondary Clarifier Return Activated Sludge (RAS) Waste Activated Sludge (WAS) Aeration Tank

Qw Xu QR Q0 Q0-Qw Xe

V, X

X0

SRT=solids retention time

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Solids Mass Balance

 Consider aeration tank and clarifier together

 Biomass in + biomass produced due to growth = biomass out  Now using the combined growth equation without limitation to

carrying capacity:

 Combining and assuming X0 and Xe to be negligible:

 

w w e w

X Q X Q Q dt dX V X Q    

X k S K S dt dX

d s

                

max

d w w s

k VX X Q S K S   

max

We will cover this in CEE 471

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David Reckhow

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Substrate Mass Balance

 Consider aeration tank and clarifier together

 Substrate in + substrate consumed by biomass = substrate out  Now using the combined substrate utilization equation without

limitation to carrying capacity:

 Combining and rearranging:

 

S Q S Q Q dt dS V S Q

w w

   

 

S S VX Y Q S K S

s

  

max

Note that effluent and waste sludge substrate concentrations are considered the same

X k S K S Y dt dS

d s

                 

max

1 

We cover this in detail in CEE 471

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Combined Mass Balances

 In summary the solids and substrate mass

balance equations are:

 These can be easily combined (left hand

terms are the same):

d w w s

k VX X Q S K S   

max

 

S S VX Y Q S K S

s

  

max

 

d w w

k S S VX Y Q VX X Q   

c

 1

The mean cell residence time, or sludge age We cover this in CEE 471

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Sludge Treatment

 Depends on type of

sludge

 Typical process train

 Thickening or

dewatering

 Conditioning  Stabilization (usually

for wastewater)

 Disposal

 Nonmechanical

methods

 Lagoons  Sand-drying beds  Freeze treatment

 Mechanical methods

 Centrifugation  Vacuum filtration  Belt filter press  Plate filters

See also Lecture #30

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 Centrifuge

From Lecture #30

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Vacuum Filter

From Lecture #30

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Belt Filter Press

From Lecture #30

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 To next lecture